I contacted my help desk and they informed me that nothing on the VPN should cause this issue. Here's what they said:
Start Menu -> Settings
Network & Internet
Scroll down to "Network and Sharing Center"
In the bottom left under "See also", select "Internet Options"
Under the "Connections" tab, check the VPN settings for any proxy. Uncheck any boxes.
Also under the "Connections" tab, check "LAN settings" for any proxy. Uncheck any boxes.
Unchecking the box that says "Automatically detect settings" is what solved the issue. Evernote is now syncing again over the VPN.
Thanks